Problem: A few families took a trip to an amusement park together. Tickets cost $$5.00$ each for adults and $$3.50$ each for kids, and the group paid $$24.00$ in total. There were $2$ fewer adults than kids in the group. Find the number of adults and kids on the trip.
Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${5x+3.5y = 24}$ ${x = y-2}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-2}$ for $x$ in the first equation. ${5}{(y-2)}{+ 3.5y = 24}$ Simplify and solve for $y$ $ 5y-10 + 3.5y = 24 $ $ 8.5y-10 = 24 $ $ 8.5y = 34 $ $ y = \dfrac{34}{8.5} $ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into ${x = y-2}$ to find $x$ ${x = }{(4)}{ - 2}$ ${x = 2}$ You can also plug ${y = 4}$ into ${5x+3.5y = 24}$ and get the same answer for $x$ ${5x + 3.5}{(4)}{= 24}$ ${x = 2}$ There were $2$ adults and $4$ kids.